U.S. patent number 10,551,633 [Application Number 15/515,426] was granted by the patent office on 2020-02-04 for diffuser plate and method for designing diffuser plate.
This patent grant is currently assigned to KURARAY CO., LTD.. The grantee listed for this patent is KURARAY CO., LTD.. Invention is credited to Masaru Karai, Atsushi Uchida.
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United States Patent |
10,551,633 |
Uchida , et al. |
February 4, 2020 |
Diffuser plate and method for designing diffuser plate
Abstract
The present invention provides a diffuser plate in a simple
structure capable of achieving optical properties with less
luminance irregularity and color irregularity and good quality of
appearance. A diffuser plate is a diffuser plate where a plurality
of microlenses are placed on a principal surface, shapes of the
plurality of microlenses along a cross-section perpendicular to the
principal surface are different from one another and do not have an
axis of symmetry. A method for designing the diffuser plate
includes steps of determining a specific reference microlens;
placing the reference microlens on the principal surface; forming a
specific phase modulation shape; and determining a shape of the
plurality of microlenses by combining the specific reference
microlens and the specific phase modulation shape.
Inventors: |
Uchida; Atsushi (Kamisu,
JP), Karai; Masaru (Kamisu, JP) |
Applicant: |
Name |
City |
State |
Country |
Type |
KURARAY CO., LTD. |
Kurashiki-shi |
N/A |
JP |
|
|
Assignee: |
KURARAY CO., LTD.
(Kurashiki-shi, JP)
|
Family
ID: |
55629852 |
Appl.
No.: |
15/515,426 |
Filed: |
September 30, 2015 |
PCT
Filed: |
September 30, 2015 |
PCT No.: |
PCT/JP2015/004961 |
371(c)(1),(2),(4) Date: |
March 29, 2017 |
PCT
Pub. No.: |
WO2016/051785 |
PCT
Pub. Date: |
April 07, 2016 |
Prior Publication Data
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|
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Document
Identifier |
Publication Date |
|
US 20170235154 A1 |
Aug 17, 2017 |
|
Foreign Application Priority Data
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|
|
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Sep 30, 2014 [JP] |
|
|
2014-201606 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G03B
21/625 (20130101); G02B 27/0012 (20130101); G02B
5/02 (20130101); G02B 5/0221 (20130101); G02B
3/0043 (20130101); G02B 27/48 (20130101); G03B
21/602 (20130101); G02B 5/0284 (20130101); G02B
5/0278 (20130101) |
Current International
Class: |
G02B
27/48 (20060101); G03B 21/625 (20140101); G03B
21/602 (20140101); G02B 27/00 (20060101); G02B
5/02 (20060101); G02B 3/00 (20060101) |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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|
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1386203 |
|
Dec 2002 |
|
CN |
|
2 120 070 |
|
Nov 2009 |
|
EP |
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2000-48613 |
|
Feb 2000 |
|
JP |
|
2004-505306 |
|
Feb 2004 |
|
JP |
|
2004-510194 |
|
Apr 2004 |
|
JP |
|
2007-25441 |
|
Feb 2007 |
|
JP |
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2007-523369 |
|
Aug 2007 |
|
JP |
|
2010-145745 |
|
Jul 2010 |
|
JP |
|
2012-47996 |
|
Mar 2012 |
|
JP |
|
2012-226300 |
|
Nov 2012 |
|
JP |
|
WO 2014/104106 |
|
Jul 2014 |
|
WO |
|
Other References
International Search Report dated Dec. 8, 2015 in PCT/JP2015/004961
filed Sep. 30, 2015. cited by applicant .
Hakan Urey et al., "Microlens-array-based exit-pupil expander for
full-color displays", Applied Optics, vol. 44, No. 23, Aug. 10,
2005, pp. 4930-4936. cited by applicant .
Combined Chinese Office Action and Search Report dated Jul. 4, 2018
in corresponding Patent Application No. 201580052717.3 (with
English Translation), 13 pages. cited by applicant .
Extended European Search Report dated May 23, 2018 in European
Patent Application No. 15847280.3, 6 pages. cited by applicant
.
Office Action dated Sep. 13, 2018, in Taiwan Patent Application No.
104132110. cited by applicant .
Frank Wippermann et al., "Beam homogenizers based on chirped
microlens arrays", dated May 14, 2007, vol. 15, No. 10, Optics
Express, pp. 6218-6231. cited by applicant .
Tung-Yu Chang et al., "Asymmetric focusing microlens array
fabricated using off-axis lithography", Microsyst Technol (2013),
pp. 861-869. cited by applicant.
|
Primary Examiner: Collins; Darryl J
Assistant Examiner: Sumlar; Journey F
Attorney, Agent or Firm: Oblon, McClelland, Maier &
Neustadt, L.L.P.
Claims
The invention claimed is:
1. A diffuser plate where a plurality of microlenses are placed on
a principal surface, wherein shapes of the plurality of microlenses
along a cross-section perpendicular to the principal surface are
different from one another and do not have an axis of symmetry,
wherein the diffuser plate is a transmissive diffuser plate, the
plurality of microlenses are convex lenses, and
0.2.ltoreq..DELTA.H.times.(n-1).times.1000/.lamda. is satisfied
where .DELTA.H [.mu.m] is a difference between a maximum height and
a minimum height of an apex of a convex surface of the plurality of
microlenses from the principal surface, n is a refractive index of
the microlens, and .lamda. [nm] is a wavelength of incidence
light.
2. The diffuser plate according to claim 1, wherein a surface shape
of each of the plurality of microlenses along the cross-section
consists only of curves without any linear side surfaces, and
wherein a shape of the plurality of microlenses is a composite
shape of one reference microlens repetitively placed on the
principal surface and a phase modulation shape having a curve
continuously varying with respect to the principal surface.
3. A diffuser plate where a plurality of microlenses are placed on
a principal surface, wherein shapes of the plurality of microlenses
along a cross-section perpendicular to the principal surface are
different from one another and do not have an axis of symmetry,
wherein the diffuser plate is a transmissive diffuser plate, the
plurality of microlenses are concave lenses, and
0.2.ltoreq..DELTA.D.times.(n-1).times.1000/.lamda. is satisfied
where .DELTA.D [.mu.m] is a difference between a maximum depth and
a minimum depth of an apex of a concave surface of the plurality of
microlenses from the principal surface, n is a refractive index of
the microlens, and .lamda. [nm] is a wavelength of incidence
light.
4. The diffuser plate according to claim 3, wherein a surface shape
of each of the plurality of microlenses along the cross-section
consists only of curves without any linear side surfaces, and
wherein a shape of the plurality of microlenses is a composite
shape of one reference microlens repetitively placed on the
principal surface and a phase modulation shape having a curve
continuously varying with respect to the principal surface.
Description
TECHNICAL FIELD
The present invention relates to a diffuser plate and a method for
designing a diffuser plate.
BACKGROUND ART
A diffuser plate using a microlens array is used as screens such as
a head-up display and a laser projector. Using a microlens array is
advantageous in that it is possible to suppress speckle noise of
laser light compared with using a diffuser plate such as a
translucent plate or a frosted glass.
Patent Literature 1 discloses an image forming device including a
diffuser plate using a laser projector that has laser light as a
light source and projects a video which is an array of a plurality
of pixels and a microlens array in which a plurality of microlenses
are placed in an array. Using a microlens array makes it possible
to appropriately diffuse incident light and flexibly design a
necessary angle of diffusion.
Patent Literatures 2 and 3 and Non Patent Literature 1 disclose a
screen using two microlens arrays. In the case of using a single
microlens array, luminance irregularity and color irregularity are
likely to occur. Patent Literatures 2 and 3 and Non Patent
Literature 1 describe that, with use of two microlens arrays, it is
possible to suppress the occurrence of luminance irregularity.
Further, Patent Literature 3 discloses that, by using one microlens
array where microlenses having different properties are placed, it
is possible to suppress the occurrence of luminance irregularity
due to diffracted light and interfering light caused by the
periodic structure.
Patent Literature 4 discloses a method for improving luminance
irregularity and color irregularity that occur due to diffraction
spots caused by the periodicity of a microstructure by placing a
piston form (raised part) having a vertical side surface on a
microlens and by randomly distributing at least one of parameters
that define the shape or position of a microstructure according to
a predetermined probability density function.
CITATION LIST
Patent Literature
PTL1: Japanese Unexamined Patent Application Publication No.
2010-145745 PTL2: Japanese Unexamined Patent Application
Publication No. 2012-226300 PTL3: Japanese Unexamined Patent
Application Publication (Translation of PCT Application) No.
2007-523369 PTL4: Japanese Unexamined Patent Application
Publication (Translation of PCT Application) No. 2004-505306
Non Patent Literature
NPL1: H. Urey and K. D. Powell, "Microlens-array-based exit-pupil
expander for full-color displays", APPLIED OPTICS Vol. 44, No. 23,
p. 4930-4936
SUMMARY OF INVENTION
Technical Problem
Patent Literature 3 does not disclose the specific shape and
placement of the microlenses for suppressing the occurrence of
luminance irregularity. Further, if a random distribution is added
simultaneously to a plurality of parameters such as the curvature
and placement of microlenses to make uniform color irregularity and
luminance irregularity, for example, speckle due to laser light is
likely to occur when the diffuser plate is used as a screen, which
raises a problem of degradation in image quality.
In Patent Literature 4, a plurality of microlenses are raised by
use of piston forms having different heights from the principal
surface of a substrate so as to add different phase differences to
the plurality of microlenses, thereby suppressing the occurrence of
diffracted light and interfering light and obtaining uniform
diffusion properties as a whole diffuser plate. However, because
the piston form stands vertically on the principal surface of the
substrate, moldability is not good, and molding defects such as
sticking of parts in the mold is likely to occur during production.
Light is scattered in a defective part on the diffuser plate, which
can result in poor appearance of an image when projected.
The present invention has been accomplished to solve the above
problems and an object of the present invention is thus to provide
a diffuser plate and a method for designing a diffuser plate in a
simple structure capable of achieving optical properties with less
luminance irregularity and color irregularity and good quality of
appearance when an image is projected.
Solution to Problem
A diffuser plate according to the present invention is a diffuser
plate where a plurality of microlenses are placed on a principal
surface, wherein shapes of the plurality of microlenses along a
cross-section perpendicular to the principal surface are different
from one another and do not have an axis of symmetry.
In the present invention, a surface shape of each of the plurality
of microlenses along the cross-section consists only of curves.
In the present invention, apexes of the plurality of microlenses
are at different positions in a direction perpendicular to the
principal surface.
In the present invention, the plurality of microlenses are arranged
in a lattice pattern on the principal surface.
In the present invention, the diffuser plate is a transmissive
diffuser plate, the plurality of microlenses are convex lenses, and
0.2.ltoreq..DELTA.H.times.(n-1).times.1000/.lamda. is satisfied
where .DELTA.H [.mu.m] is a difference between a maximum height and
a minimum height of an apex of a convex surface of the plurality of
microlenses from the principal surface, n is a refractive index of
the microlens, and .lamda. [nm] is a wavelength of incidence
light.
In the present invention, the diffuser plate is a transmissive
diffuser plate, the plurality of microlenses are concave lenses,
and 0.2.ltoreq..DELTA.D.times.(n-1).times.1000/.lamda. is satisfied
where .DELTA.D [.mu.m] is a difference between a maximum depth and
a minimum depth of an apex of a concave surface of the plurality of
microlenses from the principal surface, n is a refractive index of
the microlens, and .lamda. [nm] is a wavelength of incidence
light.
In the present invention, the diffuser plate is a reflective
diffuser plate, the plurality of microlenses are convex lenses, and
0.1.ltoreq..DELTA.H.times.1000/.lamda. is satisfied where .DELTA.H
[.mu.m] is a difference between a maximum height and a minimum
height of an apex of a convex surface of the plurality of
microlenses from the principal surface, and .lamda. [nm] is a
wavelength of incidence light.
In the present invention, the diffuser plate is a reflective
diffuser plate, the plurality of microlenses are concave lenses,
and 0.1.ltoreq..DELTA.D.times.1000/.lamda. is satisfied where
.DELTA.D [.mu.m] is a difference between a maximum depth and a
minimum depth of an apex of a concave surface of the plurality of
microlenses from the principal surface, and .lamda. [nm] is a
wavelength of incidence light.
In the present invention, a shape of the plurality of microlenses
is a composite shape of one reference microlens repetitively placed
on the principal surface and a phase modulation shape having a
curve continuously varying with respect to the principal
surface.
In the present invention, an optical axis of a microlens array
composed of the plurality of microlenses is in a direction
perpendicular to the principal surface.
A method for designing a diffuser plate according to the present
invention is a method for designing a diffuser plate where a
plurality of microlenses are placed on a principal surface, the
method including determining one or a plurality of shapes of
reference microlenses where a cross-section perpendicular to the
principal surface has an axis of symmetry; placing the plurality of
reference microlenses on the principal surface; forming a phase
modulation shape having a curve continuously varying with respect
to the principal surface; and determining a shape of the plurality
of microlenses by combining a shape of the plurality of placed
reference microlenses and the phase modulation shape.
In the present invention, a plurality of raised parts to be
disposed between the plurality of placed reference microlenses and
the principal surface are formed, and the phase modulation shape is
formed by averaging heights of the plurality of formed raised
parts.
In the present invention, the phase modulation shape along the
cross-section is a moving-average approximate curve of heights of
the plurality of formed raised parts.
In the present invention, the plurality of microlenses are arranged
in a lattice pattern on the principal surface.
Advantageous Effects of Invention
According to the present invention, it is possible to provide a
diffuser plate and a method for designing a diffuser plate in a
simple structure capable of achieving optical properties with less
luminance irregularity and color irregularity and good quality of
appearance when an image is projected.
BRIEF DESCRIPTION OF DRAWINGS
FIG. 1 is a view showing the cross-sectional profile of a
cross-section perpendicular to the principal surface of a diffuser
plate according to a first embodiment.
FIG. 2 is a view showing a shape on the principal surface of the
diffuser plate according to the first embodiment;
FIG. 3 is a flowchart showing a process of a method for producing
the diffuser plate according to the first embodiment;
FIG. 4 is a flowchart showing a design process of a microlens array
according to the first embodiment;
FIG. 5 is a view showing the cross-sectional profile of a plurality
of reference microlenses according to the first embodiment;
FIG. 6 is a view showing the cross-sectional profile of a phase
modulation shape according to the first embodiment;
FIG. 7 is a flowchart showing a mold production process of the
diffuser plate according to the first embodiment;
FIG. 8 is a view showing an image, observed by a laser microscope,
of a stamper used for production of the diffuser plate according to
an example 1;
FIG. 9A is a view showing an observation result of a transmission
image of a projector of the diffuser plate according to the example
1;
FIG. 9B is a view showing an observation result of a transmission
image of a projector of the diffuser plate according to related
art; and
FIG. 10 is a view showing diffusion angle distribution
characteristics of the diffuser plate according to the first
embodiment.
DESCRIPTION OF EMBODIMENTS
First Embodiment
Embodiments of the present invention are described hereinafter with
reference to the drawings.
(Shape of Diffuser Plate)
FIG. 1 is a view showing the cross-sectional profile of a
cross-section perpendicular to a principal surface S1 of a diffuser
plate 1 according to this embodiment. As shown in FIG. 1, the
diffuser plate 1 is an optical diffuser plate in which a plurality
of microlenses 2 are placed on the principal surface S1 of a
substrate. The plurality of microlenses 2 are arranged in a lattice
pattern on the principal surface S1. The vertical axis in FIG. 1
indicates the height of a lens shape from the principal surface S1
where the height of the principal surface S1 of the substrate is 0.
The horizontal axis in FIG. 1 indicates the position in a direction
parallel to the principal surface S1. Note that the optical axis of
a microlens array composed of the plurality of microlenses 2 is in
the direction perpendicular to the principal surface S1.
As shown in FIG. 1, the shapes of the plurality of microlenses 2
along the cross-section perpendicular to the principal surface S1
are different from one another and do not have the axis of
symmetry. The surface shape of each of the plurality of microlenses
2 along the cross-section consists only of curves. The apexes of
the plurality of microlenses 2 are at different positions in the
direction perpendicular to the principal surface S1.
FIG. 2 shows a microlens array in a unit area of about 450
.mu.m.times.480 .mu.m. The diffuser plate 1 is formed by placing
the unit areas all over the principal surface S1 of the substrate.
The vertical axis and the horizontal axis in FIG. 2 indicate the
coordinates on the principal surface S1, and the height of each
microlens from the principal surface S1 is shown by a difference in
color. In FIG. 2, as the color is closer to black, the height from
the principal surface S1 is smaller, and as the color is closer to
white, the height from the principal surface S1 is larger. It is
preferred that the plurality of microlenses 2 are arranged in a
lattice pattern on the principal surface S1 as shown in FIG. 2.
Although the plurality of microlenses 2 are arranged
in a rectangular lattice pattern in FIG. 2, the lattice pattern is
not limited to rectangular lattice, and it may be square lattice,
equilateral triangle lattice, orthorhombic lattice, parallelotope
lattice and the like.
FIG. 3 is a flowchart showing a process of a method for producing
the diffuser plate 1. A method for producing the diffuser plate 1
according to this embodiment includes a process step of designing a
microlens array that presents desired light diffusion properties
(ST100), a process step of producing a mold for the microlens array
(ST200), and a process step of transferring the shape of the
microlens array to resin by using the mold (ST300).
The process steps are sequentially described below.
(Microlens Array Design Process Step)
A microlens array design process step (ST100) in the design of the
diffuser plate 1 according to this embodiment is described
hereinafter with reference to FIG. 4. In this embodiment, a shape
of a reference microlens 3 (FIG. 5) and a phase modulation shape 4
that adds a phase difference to the reference microlens 3 (FIG. 6)
are designed separately.
First, the specification of optical physical properties
(particularly, refractive index) of materials to be used for the
diffuser plate 1, a use wavelength and necessary diffusion
properties are determined (ST110).
Next, the shape of the reference microlens 3 is designed (ST120).
The shape of the reference microlens 3 may be any shape such as
spherical and aspherical as long as it satisfies the specification
of diffusion properties required. Although the number of types of
the reference microlens 3 to be used for design of the diffuser
plate 1 is not limited, it is preferred to use a smaller number of
types within the range of satisfying the necessary characteristics.
FIG. 5 shows, as an example of the shape of the reference microlens
3, the cross-sectional profile of a microlens array in which
spherical lenses having four types of curvature are placed.
Because it is desirable that the plurality of microlenses 2 are
closely packed in the diffuser plate 1, the undersurface of the
reference microlens 3 preferably has a shape that is suitable for
close packing, such as square, rectangle or regular hexagon. Note
that, however, this does not apply in the case of adding anisotropy
to the optical properties of the diffuser plate 1, for example, and
the shape and the aspect ratio of the undersurface of the reference
microlens 3 may be set arbitrarily.
After that, the placement of the reference microlenses 3 is
determined (ST130). To be specific, the placement pattern and the
pitch of the reference microlenses 3 in a unit area on the
principal surface S1 are determined. As shown in FIG. 5, a
plurality of microlenses in different shapes may be used. Further,
as shown in FIG. 2, the reference microlenses 3 are preferably
arranged in a lattice pattern on the principal surface S1.
By periodically repeating the unit area, a necessary pattern area
can be filled. By increasing the size of a unit area and randomly
placing a plurality of types of unit areas, it is possible to
effectively reduce luminance irregularity and color irregularity.
Further, by repeating such a unit area, the amount of data required
for processing can be suppressed, and it is thereby possible to
reduce the load of data creation. As a matter of course, data for
the whole area of the microlens array may be prepared in block if a
processing machine can process a large amount of data with no
problem.
Then, the phase modulation shape 4 for adding a phase difference is
designed (ST140). In the diffuser plate 1 according to this
embodiment, a phase difference is represented by normalizing a
difference in the optical path length of light transmitted or
reflected by the microlens 2 by wavelength. In order to add a phase
difference to each of the plurality of microlenses 2, the phase
modulation shape 4 is defined separately from the shape of the
reference microlens 3. The phase modulation shape 4 may be
generated based on the average pitch, a difference in height and
the like, for example, and it may be generated by combining several
sinusoidal waves.
In this embodiment, a phase difference is randomly set by using
uniform random numbers for the plurality of microlenses 2 within a
predetermined phase difference range. First, a phase difference
that is represented by one numerical value is set for each of the
plurality of microlenses 2. In this state, a phase difference is
not continuous at the boundary of the microlenses 2. Therefore, by
averaging the phase differences of the plurality of microlenses 2
that constitute the microlens array, the phase modulation shape 4
with a three-dimensional curve where the phase difference varies
continuously is formed. FIG. 6 shows an example of the shape of the
phase modulation shape 4.
After that, the shape of the plurality of microlenses 2 is formed
(ST150). The shape of the plurality of microlenses 2 in the
microlens array to be finally formed is a composite shape of the
phase modulation shape 4 and the plurality of reference microlenses
3. Specifically, the microlens array shape as shown in FIG. 1 is
formed by combining the phase modulation shape 4 as shown in FIG. 6
and the shape of the plurality of reference microlenses 3 as shown
in FIG. 5.
The shape of the plurality of reference microlenses 3 shown in FIG.
5 is a microlens which has the axis of symmetry. On the other hand,
the phase modulation shape 4 in FIG. 6 is a three-dimensional curve
that varies continuously, which does not have the axis of symmetry.
Therefore, on the cross-section perpendicular to the principal
surface S1 of the microlens array which combines the plurality of
reference microlenses 3 and the phase modulation shape 4 as shown
in FIG. 1, each of the cross-sectional shapes of the plurality of
microlenses 2 is an asymmetric shape that does not have the axis of
symmetry.
Accordingly, the cross-sections of the plurality of microlenses 2
are different from one another, and each cross-section is
asymmetric. Note that, however, because there is a probability that
identical lenses may exist by chance, it is not excluded that
identical microlenses exist among the plurality of microlenses 2.
It is also not excluded that identical lenses are placed
intentionally. No significant problem is caused by the presence of
several identical microlenses. However, if the number of identical
lenses exceeds 10% of the number of microlenses 2 in the microlens
array, for example, it affects the properties such as luminance
irregularity, which is not desirable.
The optical properties of the diffuser plate 1 using the microlens
array composed of the plurality of microlenses 2 with asymmetric
cross-sections can be obtained by wave optics calculation based on
the scalar theory. Because there are an enormous number of
combinations for design of the most appropriate phase modulation
shape 4 and the microlens array, it is preferred to search for the
most appropriate combination by using a computer.
(Phase Difference of Plurality of Microlenses)
A transmissive diffuser plate using a microlens array is
specifically described. As shown in FIG. 6, the phase modulation
shape 4 is characterized in that its shape varies continuously. A
difference in height of the phase modulation shape 4 from the
principal surface S1 is a phase difference that is added to each of
the plurality of microlenses 2.
In the diffuser plate 1 according to this embodiment, luminance
irregularity and color irregularity that occur due to diffraction
are improved by adding a phase difference to each of the
microlenses 2. The case where the diffuser plate 1 is a
transmissive diffuser plate, and the plurality of microlenses 2 are
convex lenses is considered hereinbelow. A phase difference of the
plurality of microlenses 2 is a combination of the phase modulation
shape 4 and the shape of the reference microlens 3, and the maximum
difference in height of the apex of the plurality of microlenses 2
is .DELTA.H [.mu.m]. A phase difference corresponding to the
maximum difference in height .DELTA.H is represented as
1000.times..DELTA.H.times.(n-1)/.lamda. where n is the refractive
index of a material that forms the microlens array and .lamda. is a
wavelength [nm] of a light source used.
In order to achieve the improvement of luminance irregularity and
color irregularity, the phase difference of the plurality of
microlenses 2 needs to be set to 0.2 or more, and more preferably,
it is set to 0.5 or more. In the case where a light source has a
plurality of wavelength, a phase difference can be calculated for
the longest wavelength among the wavelengths used.
Specifically, when a difference between the maximum height and the
minimum height (maximum difference in height) of the apex of the
convex part of the plurality of microlenses 2 from the principal
surface S1 is .DELTA.H [.mu.m], the refractive index of the
microlens 2 is n, and the wavelength of incidence light is .lamda.
[nm], it is preferred to satisfy
0.2.ltoreq..DELTA.H.times.(n-1).times.1000/.lamda. and, more
preferably, 0.5.ltoreq..DELTA.H.times.(n-1).times.1000/.lamda..
Although transmissive convex lenses are used as an example above,
the case where the diffuser plate 1 is a transmissive diffuser
plate, and the plurality of microlenses 2 are concave lenses is
considered hereinbelow. In the case of transmissive concave lenses,
.DELTA.H is replaced by a difference .DELTA.D [.mu.m] between the
maximum depth and the minimum depth of the concave surface of the
plurality of microlenses 2 from the principal surface S1.
Specifically, when a difference between the maximum depth and the
minimum depth of the apex of the concave surface of the plurality
of microlenses 2 from the principal surface S1 is .DELTA.D [.mu.m],
the refractive index of the microlens 2 is n, and the wavelength of
incidence light is .lamda. [nm], it is preferred to satisfy
0.2.ltoreq..DELTA.D.times.(n-1).times.1000/.lamda. and, more
preferably, 0.5.ltoreq..DELTA.D.times.(n-1).times.1000/.lamda..
The case where the diffuser plate 1 is a reflective diffuser plate,
and the plurality of microlenses 2 are convex lenses is considered
below. Note that, in the case of a reflective diffuser plate, the
diffusion pattern formed on the surface does not transmit light and
it is thus not a lens in a strict sense; however, the lens-like
concave-convex shape is also referred to as "microlens" in this
specification.
Incidence light is reflected by the surface of the microlens array
with the distribution of the height of the apex of the convex part
of the plurality of microlenses 2, and thereby an optical path
difference is generated between forward and return paths, and a
phase difference is generated between the plurality of microlenses
2. A phase difference corresponding to a difference .DELTA.H
between the maximum height and the minimum height of the apex of
the convex part of the plurality of microlenses 2 from the
principal surface S1 at this time is represented as
1000.times.2.DELTA.H/.lamda..
In order to achieve the improvement of luminance irregularity and
color irregularity, the phase difference needs to be set to 0.2 or
more, and more preferably, it is set to 0.5 or more, just like the
case of a transmissive type.
Specifically, when a difference between the maximum height and the
minimum height of the apex of the convex surface of the plurality
of microlenses 2 from the principal surface S1 is .DELTA.H [.mu.m],
and the wavelength of incidence light is .lamda. [nm], it is
preferred to satisfy 0.1.ltoreq..DELTA.H.times.1000/.lamda. and,
more preferably, 0.25.ltoreq..DELTA.H.times.1000/.lamda..
The case where the diffuser plate 1 is a reflective diffuser plate,
and the plurality of microlenses 2 are concave lenses is considered
below. In the case of using concave lenses in a reflective type,
.DELTA.H is replaced by a difference .DELTA.D between the maximum
depth and the minimum depth of the concave part of the plurality of
microlenses 2 from the principal surface S1, which is the same as
the case of using concave lenses in a transmissive type.
When a difference between the maximum depth and the minimum depth
of the apex of the concave surface of the plurality of microlenses
2 from the principal surface S1 is .DELTA.D [.mu.m], and the
wavelength of incidence light is .lamda. [nm], it is preferred to
satisfy 0.1.ltoreq..DELTA.D.times.1000/.lamda. and, more
preferably, 0.25.ltoreq..DELTA.D.times.1000/.lamda..
The maximum difference in height .DELTA.H in the microlens array
may be set for the whole pattern area of the microlens array, or
the maximum difference in height .DELTA.H may be set in a certain
unit area, and it may be repeated periodically or randomly.
For producing a microlens array from design data, many processing
method such as machining, photolithography using a mask, maskless
photolithography, etching, laser ablation and the like can be used.
By producing a mold with use of such a technique and molding a
resin with use of the mold, the diffuser plate 1 having the
microlens array is produced. The mold can be directly used as a
reflective diffuser plate. A molding method of the diffuser plate 1
may be appropriately selected from many molding methods including
roll-to-roll molding, thermal press molding, molding using
ultraviolet curable resin, and injection molding. In the case of
using it as a reflective diffuser plate, a reflective coating such
as Al may be formed on the lens surface having the curvature of the
microlens array.
(Mold Production Process Step and Molding Process Step)
Hereinafter, a mold production process step (ST200) that produces a
mold by laser-scanning maskless lithography and electroforming, and
a resin molding process step (ST300) that produces the diffuser
plate 1 by molding using the produced mold and ultraviolet curable
resin are described in more detail with reference to FIGS. 3 and
7.
The maskless lithography consists of a resist coating process step
(ST210) that applies photoresist onto a substrate, an exposure
process step (ST220) that exposes a fine pattern onto the
photoresist, and a development process step (ST230) that develops
the photoresist after exposure and obtains a master having the fine
pattern.
First, in the resist coating process step (ST210), positive
photoresist is applied on top of a substrate. The applied
photoresist film may have any thickness as long as it is equal to
or more than the height of the fine pattern to be formed. It is
preferred to perform baking of the applied film at a temperature of
70.degree. to 110.degree. C.
Next, in the exposure process step (ST220), a laser beam scans and
is applied to the photoresist coated in the coating process step,
thereby exposing the photoresist. The wavelength of the laser beam
can be selected according to the type of photoresist, and it may be
selected from 351 nm, 364 nm, 458 nm, 488 nm (the oscillation
wavelength of an Ar+ laser), 351 nm, 406 nm, 413 nm (the
oscillation wavelength of a Kr+ laser), 352 nm, 442 nm (the
oscillation wavelength of a He--Cd laser), 355 nm, 473 nm (the
pulse oscillation wavelength of a semiconductor-pumped solid-state
laser), 375 nm, 405 nm, 445 nm, 488 nm (semiconductor laser) and
the like, for example.
In the exposure process step (ST220) of the microlens 2, a laser
beam scans the resist, modulating the laser power to a value
determined by the shape of the microlens 2 and the resist
sensitivity. Laser light is concentrated through an objective lens
and brought to a focus on the resist. A laser spot on the resist
has Gaussian distribution with a finite diameter in general.
Therefore, the distribution of the quantity of light exposed to the
resist is not step-like even when the laser power is changed in
steps, and the light exposure distribution has a certain slope. By
using such a property of laser exposure, a smooth slope shape can
be formed.
A phase difference between one microlens 2 and the adjacent
microlens 2 (which corresponds to a difference in lens height from
the principal surface S1) becomes larger by increasing a difference
in laser power applied to the microlenses 2 adjacent to each other
in the exposure process step. However, if a difference in laser
power is too large, a region in which the lens shape near the
boundary of the adjacent microlenses 2 is deviated from a designed
value becomes larger. Therefore, in order to obtain the diffusion
angle distribution which is the same as that of the optical design
result, it is desirable to set a difference in height between the
adjacent microlenses 2 within a specified range.
In this embodiment, the maximum difference in height .DELTA.H of
the microlens array is a combination of the maximum difference in
height of the phase modulation shape 4 and a difference in height
caused by a difference in shape between the plurality of reference
microlenses 3. When the above-described phase difference normalized
by wavelength is set to 1, the average of phase differences of the
plurality of microlenses 2 is 0.5. Thus, the plurality of
microlenses 2 on the diffuser plate 1 has a phase difference of 1/2
wavelength on average, which is desirable because diffracted light
is suppressed.
Then, in the development process step (ST230), the photoresist
after exposure is developed. The development of the photoresist may
be performed by various known methods. There is no particular limit
to a developer to be used, and an alkaline developer such as
tetramethylammonium hydroxide (TMAH), for example, may be used.
Further, in the development process step (ST230), the photoresist
is removed depending on light exposure, and the fine pattern shape
of the photoresist is formed. For example, in the exposure process
step (ST220), using positive resist, by the laser power
corresponding to the shape of concave lenses, a master of the
microlens 2 where the concave lens shape is formed in the
photoresist is obtained.
Then, in the electroforming process step (ST240), a metal film is
formed, by vapor deposition of nickel metal or the like, on the
surface of the photoresist having the fine pattern formed by the
exposure and development process steps by maskless
photolithography, and thereby a mold is produced.
In the electroforming process step (ST240), conducting is performed
first on the surface of the photoresist having the fine pattern by
vapor deposition of nickel metal or the like. Next, by
electroforming, nickel is deposited into plate form with a desired
thickness on the surface of the vapor-deposited nickel film.
After that, in the removal process step (ST250), the nickel plate
formed in the electroforming process step (ST240) is separated from
the photoresist master, and thereby a mold (stamper) with the
convex lens shape to which the concave lens shape on the
photoresist is inversely transferred is obtained. In the case where
the concave lens shape is required, the electroforming process step
is performed again.
Then, in the resin molding process step (ST300), resin is molded by
using the stamper produced in the mold production process step
(ST200).
To be specific, an appropriate amount of photocurable resin, for
example, is first applied on top of the surface of the stamper.
Next, a base material is placed on the photocurable resin.
Specifically, the base material is placed on top of the
photocurable resin by pressing the base material against the
photocurable resin with a hand roller and removing excess
photocurable resin. Then, ultraviolet light is applied from the
base material side to cure the photocurable resin. Note that a
material that can transmit light such as ultraviolet light is used
for the base material. After that, the base material is separated
from the stamper. On the base material separated from the stamper,
a photocurable resin layer is formed. On the photocurable resin
layer, the stamper structure is inversely transferred.
In the case of using the microlens array as a reflective diffuser
plate 1, an aluminum reflective coating may be vacuum-deposited on
the surface of a member where the microlens array is formed, for
example, so that incidence light is reflected on the aluminum
surface. Further, in the case of a member where the microlens array
is formed only on one surface of a substrate, light may be incident
to the flat surface side of the substrate and reflected on the
microlens array surface where the aluminum reflective coating is
formed.
On the other hand, a structure in which light is incident to the
microlens array surface where the reflective coating is not formed
and reflected on the flat surface side where the reflective coating
is formed can be also used as the diffuser plate 1. Further, a
substrate where microlens arrays are formed on both sides may have
a structure in which the thickness of a reflective coating on the
incidence side is adjusted to function as a half mirror and the
underside surface has a reflectivity of substantially 100%, so that
it serves as the diffuser plate with two microlens arrays on both
of the front and back surfaces. A protective coating may be further
formed to protect the aluminum reflective coating where needed.
In the diffuser plate 1 according to the present invention, a phase
difference is added to each of the plurality of microlenses 2, and
the phase modulation shape 4 that adds the phase difference has a
continuous shape, and thereby the plurality of microlenses 2 do not
have the axis of rotation symmetry like a typical lens or the axis
of symmetry like a toroidal lens on the cross-section perpendicular
to the principal surface S1, and it has an asymmetric
cross-section.
In the microlens array that is composed of the plurality of
microlenses 2 with the asymmetric cross-section, the adjacent
microlenses 2 are smoothly connected. By reducing scattered light
in a connection between the adjacent microlenses 2, it is possible
to improve the quality of appearance of the diffuser plate 1.
Further, because a phase difference is added to each of the
plurality of microlenses 2, luminance irregularity and color
irregularity due to diffraction and interference can be reduced
when the pitch of the microlenses 2 is as narrow as several hundred
.mu.m or less. It is thereby possible to provide the diffuser plate
that achieves the optical properties with less luminance
irregularity and color irregularity and the good quality of
appearance.
Example
The present invention is described in further detail based on
examples of the diffuser plate 1 according to this embodiment.
In the diffuser plate 1 according to this example, the phase
modulation shape 4 and the plurality of reference microlenses 3
were designed separately from each other in the microlens array
composed of the plurality of microlenses 2 on the principal surface
S1 as described above.
The phase modulation shape 4 was set for the whole microlens array.
In the phase modulation shape 4, the maximum difference in height
from the principal surface S1 for adding a phase difference was
.DELTA.H=1.5 .mu.m. On the principal surface S1, a raised height
(raised part) for adding a phase difference was set by generating
uniform random numbers corresponding to the respective positions of
the plurality of microlenses 2. However, merely setting different
raised heights for the plurality of microlenses 2 results in
discontinuity of a phase difference between the adjacent
microlenses 2. Therefore, the continuous phase modulation shape 4
was formed by moving-average processing of the raised height set
for each of the plurality of microlenses 2. FIG. 6 shows a part of
the designed phase modulation shape 4.
The shape of the reference microlens 3 is described next. The lens
shape of the reference microlens 3 may be a typical rotationally
symmetric shape and, in this case, the cross-section of the
reference microlens 3 is represented by the following expression
(1) where C is a curvature [1/.mu.m], K is a conic constant, r is a
distance from the central axis, and z is a sag with respect to the
point of intersection between the central axis and the lens
surface. The curvature C is represented as C=1/R, using a curvature
radius R.
.times..times. ##EQU00001##
The cross-sectional shape of the reference microlens 3 used in the
diffuser plate 1 of this example is represented by the following
expression (2). In this case, the reference microlens 3 is a
toroidal lens having a rectangular undersurface, and the curvature
is defined in each of the x-direction and the y-direction. With the
central axis of the lens as the point of origin, r.sub.x is a
distance from the central axis in the x-direction, r.sub.y is a
distance from the central axis in the y-direction, C.sub.x is a
curvature [1/.mu.m] in the x-direction (x-z plane), and C.sub.y is
a curvature [1/.mu.m] in the y-direction, K.sub.x of (x-z plane) is
a conic constant in the x-direction (x-z plane), K.sub.y is a conic
constant in the y-direction (y-z plane).
.times..times..times..times..times..times. ##EQU00002##
In the diffuser plate 1 of this example, the pitch of the plurality
of microlenses 2 was fixed to Px=30 .mu.m and Py=32 .mu.m. The
plurality of reference microlenses 3 had four types of curvature
radii in the x-direction and three types of curvature radii in the
y-direction. In the diffuser plate 1 of this example, total twelve
types of reference microlenses 3 that combine the curvature radii
in the x-direction and the y-direction were randomly selected using
uniform random numbers and placed on the principal surface S1. The
reference microlens 3 was designed to be a spherical lens
(K.sub.x=0) with the curvature radius R.sub.x[.mu.m] of 52.9, 58.5,
69.8, 77.4 in the x-direction and an aspherical lens
(K.sub.y=-0.45) with the curvature radius R.sub.y[.mu.m] of 28.2,
31.2, 34.6 in the y-direction. Further, the height of the lowest
part was a reference height in all of the reference microlenses
3.
The shape of the plurality of microlenses 2 in the microlens array
is a composite shape of the phase modulation shape 4 and the shapes
of the plurality of reference microlenses 3. FIG. 2 shows an
example of the shape of the plurality of microlenses 2 when it is
designed in the area of about 450 .mu.m.times.480 .mu.m. The shape
of the plurality of microlenses 2 that constitute the microlens
array is a shape that overlaps the plurality of reference
microlenses 3 having the axis of symmetry and the phase modulation
shape 4 not having the axis of symmetry or the point of symmetry.
Therefore, each of the plurality of microlenses 2 that constitute
the microlens array has an asymmetric cross-section.
The whole microlens array area of about 60 mm.times.80 mm on the
surface of the diffuser plate 1 was designed based on the above
facts (ST100). Using this design data, a stamper in which a
microlens array shape having a plurality of convex lenses was
formed was obtained after the above-described mold production
process step (ST200). FIG. 8 shows an observed image of the lens
shape of this stamper by a confocal laser microscope. As shown in
FIG. 8, a plurality of convex lens shapes with phase differences
were formed.
Then, molding using photocurable resin was performed using the
stamper shown in FIG. 8. A polycarbonate film with a thickness of
0.3 mm was used as a base material, and acrylic photocurable resin
with a refractive index of 1.52 was poured between the stamper and
the base material and molded, thereby producing the diffuser plate
1.
FIGS. 9A and 9B show results of projecting an image, by a projector
(PK301 manufactured by Optoma), on the diffuser plate 1 of this
example obtained by molding and taking the transmission image of
the diffuser plate 1 by a digital camera. The distance between the
diffuser plate 1 and the projector was 10 cm, so that the focal
point of the projector was at the position of the diffuser plate 1.
The image was taken by the digital camera by focusing on the
diffuser plate 1 from the direction horizontally shifted by
40.degree. from the front.
FIG. 9A is a result of projecting an image on the diffuser plate 1
according to this example, and FIG. 9B is a result of projecting an
image on the diffuser plate 1 according to related art, composed of
a microlens array where the phase modulation shape 4 was a simple
raised shape for each reference microlenses 3. Comparison shows
that the graininess of the image was significant in the one
according to related art (FIG. 9B), and the graininess was reduced
and the quality of appearance was improved in the diffuser plate 1
according to this example (FIG. 9A).
FIG. 10 is a result of measuring the diffusion angle distribution
of transmitted light intensity of the diffuser plate 1 by using a
luminance meter (BM-7 manufactured by Topcon Corporation) and a
goniometer stage. In FIG. 10, H indicates the diffusion angle
distribution in the horizontal direction and V indicates the
diffusion angle distribution in the vertical direction. Collimated
light of a white LED was used as a light source, and light was
vertically incident on the diffuser plate 1. Luminance irregularity
was small in the diffuser plate 1 according to this example, and
Luminance irregularity was reduced to the level better than that of
the related art, and the quality of appearance of the projected
image was also improved. Further, the diffusion properties of the
diffuser plate 1 were properties close to top-hat and centering on
the front (0.degree.), and the optical axes of incident light and
outgoing light substantially coincide.
It should be noted that the present invention is not limited to the
above-described exemplary embodiment and may be varied in many ways
within the scope of the present invention. For example, the
microlenses 2 placed on the diffuser plate 1 are not limited to
transmissive lenses. On the principal surface S1 of the reflective
diffuser plate 1, a light diffusion pattern having the same
concave-convex shape as the microlens 2 may be formed in a lattice
pattern just like in the microlens 2.
This application is based upon and claims the benefit of priority
from Japanese patent application No. 2014-201606, filed on Sep. 30,
2014, the disclosure of which is incorporated herein in its
entirety by reference.
REFERENCE SIGNS LIST
1 DIFFUSER PLATE 2 MICROLENS 3 REFERENCE MICROLENS 4 PHASE
MODULATION SHAPE
* * * * *